Thin obstacle problems and multiple valued minimal graphs

In this talk I will present some recent results on the analysis of the free boundary for the thin obstacle problem, in connection with the theory of stationary varifolds which are parametrized as graphs of multiple valued functions. In particular, I will focus on the global structure of the free boundary and on the finiteness of the local measure. All the results are in collaboration with M. Focardi (Uni. Firenze).